What is the solution for y^{''}-9y=1,y^'(0)=10 ?

The solution for y^{''}-9y=1,y^'(0)=10 is y=(e^{3t}(10+3c_{2}))/3+c_{2}e^{-3t}-1/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-9y=1,y^'(0)=10

y^{^{''}} - 9 y = 1, y^{^{'}} (0) = 10

y = \frac{e ^{3 t} ( 10 + 3 c _{2} )}{3} + c_{2} e^{- 3 t} - \frac{1}{9}

Solution steps

y^{''} (t) - 9 y = 1

Solve linear ODE:

y = \frac{e ^{3 t} ( 10 + 3 c _{2} )}{3} + c_{2} e^{- 3 t} - \frac{1}{9}

y = \frac{e ^{3 t} ( 10 + 3 c _{2} )}{3} + c_{2} e^{- 3 t} - \frac{1}{9}

What is the solution for y^{''}-9y=1,y^'(0)=10 ?
The solution for y^{''}-9y=1,y^'(0)=10 is y=(e^{3t}(10+3c_{2}))/3+c_{2}e^{-3t}-1/9